A train,after travelling 50 , km,meets with a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the normal speed of the train be $v \, km/hr$.
Let the distance between the point of the first accident $(C)$ and the destination $(B)$ be $d

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) Let the normal speed of the train be $v \, km/hr$.
Let the distance between the point of the first accident $(C)$ and the destination $(B)$ be $d \, km$.
When the accident occurs at $C$,the train travels the remaining distance $d$ at $\frac{3}{4}v$ speed. The time taken is $\frac{d}{\frac{3}{4}v} = \frac{4d}{3v}$.
The time that would have been taken at normal speed is $\frac{d}{v}$.
The delay is $\frac{4d}{3v} - \frac{d}{v} = \frac{d}{3v} = 35 \, minutes = \frac{35}{60} \, hours = \frac{7}{12} \, hours$. So,$\frac{d}{v} = \frac{7}{12} 	imes 3 = \frac{7}{4} \, hours \dots (1)$.
When the accident occurs $72 \, km$ further at $D$,the remaining distance is $(d - 72) \, km$.
The delay is $\frac{d-72}{\frac{3}{4}v} - \frac{d-72}{v} = 15 \, minutes = \frac{15}{60} \, hours = \frac{1}{4} \, hours$.
$\frac{d-72}{v} (\frac{4}{3} - 1) = \frac{1}{4} \implies \frac{d-72}{v} 	imes \frac{1}{3} = \frac{1}{4} \implies \frac{d-72}{v} = \frac{3}{4} \dots (2)$.
Subtracting $(2)$ from $(1)$: $\frac{d}{v} - \frac{d-72}{v} = \frac{7}{4} - \frac{3}{4} = 1 \implies \frac{72}{v} = 1 \implies v = 72 \, km/hr$.

Similar Questions

$A$ and $B$ walk around a circular track. They start at $8\, a.m.$ from the same point in opposite directions. $A$ and $B$ walk at a speed of $2\, \text{rounds per hour}$ and $3\, \text{rounds per hour}$ respectively. How many times shall they cross each other before $9.30\, a.m.$?

$A$ person has to travel from point $A$ to point $B$ in a certain time. Travelling at a speed of $5 \, km/h$,he reaches $48 \, min$ late,and while travelling at a speed of $8 \, km/h$,he reaches $15 \, min$ early. What is the distance from point $A$ to $B$ (in $km$)?

$A$ train $100 \, m$ long takes $3 \frac{3}{5} \, s$ to cross a man walking at the rate of $6 \, km/h$ in a direction opposite to that of the train. Find the speed of the train in $km/h$.

$A$ man travelled a distance of $80\, km$ in $7\, hours$,partly on foot at the rate of $8\, km/h$ and partly on bicycle at $16\, km/h$. The distance travelled on foot is (in $km$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module